Adsorption density coefficient

Effect of PVA Molecular Weight on Adsorbed Layer Thickness. Figure 4 shows the variation of reduced viscosity with volume fraction for the bare and PVA-covered 190nm-size PS latex particles. For the bare particles, nre(j/ is independent of and the value of the Einstein coefficient is ca. 3.0. For the covered particles, rired/ t increases linearly with tp. Table IV gives the adsorbed layer thicknesses calculated from the differences in the intercepts for the bare and covered particles and determined by photon correlation spectroscopy, as well as the root-mean-square radii of gyration of the free polymer coil in solution. The agreement of the adsorbed layer thicknesses determined by two independent methods is remarkable. The increase in adsorbed layer thickness follows the same dependence on molecular weight as the adsorption density, i.e., for the fully hydrolyzed PVA s and... 

Honeyman, B. D., and J. O. Leckie (1986), "Macroscopic Partitioning Coefficient for Metal Ion Adsorption Proton Stoichiometry at Variable pH and Adsorption Density", in J. A. Davis and K. F. Hayes, Eds., Geochemical Processes at Mineral Surfaces, ACS Symposium, Washington, DC. 

In their description of metal ion adsorption, Benjamin and Leckie used an apparent adsorption reaction which included a generic relationship between the removal of a metal ion from solution and the release of protons. The macroscopic proton coefficient was given a constant value, suggesting that x was uniform for all site types and all intensities of metal ion/oxide surface site interaction. Because the numerical value of x is a fundamental part of the determination of K, discussions of surface site heterogeneity, which are formulated in terms similar to Equation 4, cannot be decoupled from observations of the response of x to pH and adsorption density. As will be discussed later, It is not the general concept of surface-site heterogeneity which is affected by what is known of x> instead, it is the specific details of the relationship between K, pH and T which is altered. 

In addition, x is generally not constant and appears to exhibit some dependency on pH and adsorption density (T). Cation coefficients are generally greater than one, although there are some marked exceptions (e.g., Cd/a-FeOOH or Na-montmorillonite). In contrast, the absolute value of net proton coefficients for anions are generally between zero and one. The negative value of x for anions indicates that anion adsorption results in an overall removal of protons from solution. 

Isotherm Subtraction. A second method (7) of determining the net proton coefficient from adsorption data is an adaptation of the thermodynamics of linked functions as applied to the binding of gases to hemoglobin (19). The net proton coefficient determined by this method is designated, Xp- The computational procedure makes a clear distinction between the influence of adsorption density and pH on the magnitude of the net proton coefficient. The fundamental equation used in the calculation of Xp is... 

Figure 4. Kurbatov a) proton and b) partitioning coefficients as a function of adsorption density.

The observation that the macroscopic proton coefficient is a function of adsorption density and pH has several implications for macroscopic modeling of cation and anion adsorption. The dependency of x on pH and T affects 1) the relationship of the macroscopic partitioning coefficient to pH and adsorption density, 2) the notion of metal ion preferences for a particular surface in systems with multiple solid phases, 3) the accuracy of predictive models when used over a range of adsorption density and pH values, and 4) conclusions about site heterogeneity based upon partitioning expressions which use constant proton coefficients. 

P=f(Xp. pH). As described above, the magnitude of P is inexorably linked to the variations of x with pH and adsorption density. However, the response of x (and P) to T and pH varies among hydrous oxides. For example, Figure 9a shows the instantaneous (isotherm) proton coefficient (xp) "zones" determined for Cd ion adsorption onto (am)Fe20o O, a-A O and oc-TiC. The zones are defined by the calculated proton coefficients determined for a range of pH values and adsorption density. The "thickness" of each zone gives a qualitative comparison of the pH dependency of Xp at each adsorption... 

Figure 10. Comparison of calculated and observed adsorption densities for Cd(II) adsorption on OI-AI2O3. A single set of Kurbatov coefficients is used for the entire range of adsorption densities.

The incorporation of Xn(pH 0 into macroscopic mass-action expressions for adsorption has shown not only that K is not a unique function of T at adsorption densities greater than i but that K is also not unique below T. In both cases it is due to the dependence of the macroscopic partitioning coefficient on pH (Figure 13). 

The information in Figure 14 was produced in the following way. The slope (or the Kurbatov coefficients shown in Table V) and position of the fractional absorption gdges in Figure 3 were used as the criteria of model fit. Kcd an< CdOH were used as the fitting parameters and all other parameters were held constant. Consequently, the intrinsic constants shown in Figure 14a represent best fit parameters and, given that all other surface and solution association constants are invariant, constitute a unique solution set for each adsorption density. 

The same line of reasoning can be applied to the desorption term in Eq. 4.18 after replacing its left side with -d(SRx - [SR])/dt (to which it is equal because of mole balance) and letting p(k) become a probability density function for the rate coefficient k. If Eq. 4.23 is chosen again to represent the distribution of desorption rate coefficients, and if the coefficient of variation (although not necessarily the mean or the variance) is assumed to be the same as for the distribution of adsorption rate coefficients, then d[SR]/dt for the desorption process will also be proportional to... 

Note. tb is the breakthrough time at the outlet concentration cx = 10-5 mg/dm3 Wc is the kinetic adsorption capacity / e is effective overall adsorption rate coefficient m0 is the weight of bed, and ph is the bulk density of carbon bed. 

Both Eqs 4.16 and 4.17 predict that when adsorption density (Z/a ) is high, the interfacial tension coefficient is low. For the same surface area per chain, longer copolymer chains are predicted to be more efficient. The expressions of Z/a can be obtained, for both wet and dry brushes, as a function of the copolymer chemical potential, ji. The ratio was found to depend on... 

A limiting step of the etching is CO desorption into the gas phase, and so steady-state carbon surface coverage with the C 0 groups can be found by assuming d9/dt = 0. Here, o and i are O and ion densities near the caibon surface (at the plasma-sheath edge), and is the O adsorption rate coefficient. 

The slope of the Tafel curve drj/d log / is only one of the criteria that are required to determine the mechanism of the h.e.r., since different mechanisms, involving different r.d.s. often have the same Tafel slope. Parameters that are diagnostic of mechanism are the transfer coefficient, the reaction order, the stoichiometric number, the hydrogen coverage, the exchange current density, the heat adsorption, etc. 

For alkali modified noble and sp-metals (e.g. Cu, Al, Ag and Au), where the CO adsorption bond is rather weak, due to negligible backdonation of electronic density from the metal, the presence of an alkali metal has a weaker effect on CO adsorption. A promotional effect in CO adsorption (increase in the initial sticking coefficient and strengthening of the chemisorptive CO bond) has been observed for K- or Cs-modified Cu surfaces as well as for the CO-K(or Na)/Al(100) system.6,43 In the latter system dissociative adsorption of CO is induced in the presence of alkali species.43... 

This backdonation of electron density from the metal surface also results in an unusually low N-N streching frequency in the a-N2 state compared to the one in the y-N2 state, i.e. 1415 cm 1 and 2100 cm"1, respectively, for Fe(l 11)68. Thus the propensity for dissociation of the a-N2 state is comparatively higher and this state is considered as a precursor for dissociation. Because of the weak adsorption of the y-state both the corresponding adsorption rate and saturation coverage for molecular nitrogen are strongly dependent on the adsorption temperature. At room temperature on most transition metals the initial sticking coefficient does not exceed 10 3. 

In model equations, Uf denotes the linear velocity in the positive direction of z, z is the distance in flow direction with total length zr, C is concentration of fuel, s represents the void volume per unit volume of canister, and t is time. In addition to that, A, is the overall mass transfer coefficient, a, denotes the interfacial area for mass transfer ifom the fluid to the solid phase, ah denotes the interfacial area for heat transfer, p is density of each phase, Cp is heat capacity for a unit mass, hs is heat transfer coefficient, T is temperature, P is pressure, and AHi represents heat of adsorption. The subscript d refers bulk phase, s is solid phase of adsorbent, i is the component index. The superscript represents the equilibrium concentration. 

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